Direct product of cyclic group of prime-square order and cyclic group of prime-square order
This article is about a family of groups with a parameter that is prime. For any fixed value of the prime, we get a particular group.
View other such prime-parametrized groups
- It is the external direct product of two copies of the cyclic group of prime-square order, i.e., it is the group .
- It is the homocyclic group of order and exponent .
|Value of prime number||Corresponding group|
|2||direct product of Z4 and Z4|
|3||direct product of Z9 and Z9|
|5||direct product of Z25 and Z25|
This finite group has order p^4 and has ID 2 among the groups of order p^4 in GAP's SmallGroup library. For context, there are groups of order p^4. It can thus be defined using GAP's SmallGroup function as:
For instance, we can use the following assignment in GAP to create the group and name it :
gap> G := SmallGroup(p^4,2);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [p^4,2]
or just do:
to have GAP output the group ID, that we can then compare to what we want.
|Description||Functions used||Mathematical comments|
|DirectProduct(CyclicGroup(p^2),CyclicGroup(p^2))||DirectProduct and CyclicGroup|